The three objectives of this theoretical study of DNA supercoiling are: (1) Developing a general dynamic scheme capable of millisecond simulations for a macroscopic polymer subject to hydrodynamics modeled by curve-fitting techniques. (2) Developing an extension of the homogeneous, elastic rod energy model for dynamic simulations of DNA to incorporate sequence and protein-binding effects. (3) Studying systematically the global structural and dynamic features of DNA associated with site juxtaposition, the rate at which two sites along the DNA come into close spatial proximity as a result of supercoiling; this general problem has many applications to genetic processes where juxtaposition is a prerequisite for the reaction and where DNA supercoiling plays mechanistic roles, such as transcription regulation, recombination, and topoisomerase activity. Unfortunately, it is very difficult to study these fast processes by instrumentation. Our juxtaposition simulations will be performed for average-sequence DNA, plasmids of specific composition, and DNA bound to proteins, with a major focus on site-synapsis kinetics in the recombination of resolvase. The studies will help clarify the role of supercoiling in processes involving supercoiled DNA and DNA/protein interactions: How does supercoiling enhance juxtaposition with respect to linear DNA, and how do juxtaposition times depend on the site separation, DNA length, salt concentration, DNA sequence, and bound proteins? Simulations will also address specific biological hypotheses of supercoiled-directed mechanisms concerning the experimentally-measured dependence of synapsis on the superhelical density, the failure of synapsis for nicked circular DNA, the indispensability of supercoiling in site-specific recombinations where three sites synapse but not two, the orientation selectivity in recombination reactions that depend on supercoiling, the fast and topologically-specific juxtaposition in resolvase, and the kinetics of site synapsis in resolvase. New modeling and simulation protocols for studying biologically interesting processes of supercoiled DNA in solution that are large-scale and long-time will also result. The global characteristics of the double helix explored here - interactions among distant DNA sites, supercoiling dynamics and energetics - play important roles in the action of the metabolically essential enzymes that interact with DNA. Further progress in our understanding of superhelicity has many practical benefits: Understanding the dependence of juxtaposition rates on external and internal factors might also ultimately help design conditions to enhance recognition among sites within long DNA and hence also between DNA and proteins. The fundamental importance of DNA topoisomerases associated with supercoiling and knotting has led to much research on topoisomerase inhibitors that act as anticancer or antibacterial drugs. Thus, any new structural and dynamic information on supercoiling and DNA-protein interactions may ultimately contribute to these pharmaceutical applications.